Optical element

ABSTRACT

A complex amplitude type spatial optical modulation element, with which the amount of generation of 0th-order diffraction light is low. An optical element is arranged by aligning a plurality of three-dimensional cells C 1 (x, y) two-dimensionally on an XY plane. Each individual cell is made of a light transmitting material and has a specific amplitude and a specific phase defined therein. The individual cell has a specific optical characteristic such that when predetermined incident light is provided from the upper surface of the cell, reflection emitted light, with which amplitude and phase of the incident light have been changed in accordance with the specific amplitude and the specific phase defined in the cell, is obtained from the upper surface of the cell.

This application is a divisional of application Ser. No. 11/042,798filed Jan. 25, 2005 now U.S. Pat. No. 7,221,496 claims the benefitthereof and incorporates the same by reference.

BACKGROUND OF THE INVENTION

The present invention relates to an optical element and, moreparticularly, relates to an optical element suitable for constructing acomplex amplitude type spatial optical modulator by assembling a lot ofthree-dimensional cells and for recording a stereoscopic image as ahologram.

A holographic technique is conventionally known as a method forrecording a stereoscopic image on a medium and reconstructing thisimage. A hologram produced by this method is used in various fields,such as ornamental art or anti-counterfeit seals. In order to opticallyproduce the hologram, it is common to record the interference fringebetween object light reflected from an object and reference light on aphotosensitive medium. A laser beam superior in coherence is usuallyused as a light source for the object light and the reference light.Generally, the motion of electromagnetic radiation, such as light, canbe regarded as the propagation of a wave front provided with amplitudeand a phase, and it can be said that the hologram is an optical elementthat functions to reconstruct such a wave front. Therefore, it isnecessary to record information for accurately reconstructing theamplitude and phase of the object light at each position in space on therecording medium of the hologram. If interference fringes generated bythe object light and the reference light are recorded on thephotosensitive medium, information that includes both the phase and theamplitude of the object light can be recorded, and, by projectingillumination reconstructing light equivalent to the reference light ontothe medium, a part of the illumination reconstructing light can beobserved as light provided with a wave front equivalent to the objectlight.

If the hologram is produced by an optical method using a laser beam orthe like in this way, the phase and amplitude of the object light can berecorded only as interference fringes resulting from interferencebetween the object light and the reference light. The reason is that thephotosensitive medium has a property of being photosensitized inaccordance with light intensity. On the other hand, a technique ofproducing a hologram by computations with use of a computer has recentlybeen put to practical use. This technique is called a “CGH”(Computer-Generated Hologram) method, in which the wave front of objectlight is calculated by use of a computer, and its phase and itsamplitude are recorded on a physical medium according to a certainmethod so as to produce a hologram. The employment of this computationalholography, of course, enables the recording of an image as interferencefringes between object light and reference light, and, in addition,enables the recording of information for the phase and amplitude of theobject light directly onto a recording surface without using thereference light.

For example, an optical element, comprising a set of a plurality ofthree-dimensional cells, is disclosed in U.S. Pat. No. 6,618,190. Thisoptical element functions as a complex amplitude type spatial opticalmodulator, and by using this art, a hologram can be arranged by the setof three-dimensional cells and a three-dimensional image can berecorded. A specific amplitude and a specific phase are defined in eachindividual three-dimensional cell of the optical element disclosed inU.S. Pat. No. 6,618,190, and when a predetermined incident light isprovided to an individual cell, emitted light, with which the amplitudeand phase of the incident light have been changed in accordance with thespecific amplitude and specific phase defined in the cell, is obtained.That is, each individual cell has unique optical characteristics andfunctions as an element (complex amplitude type spatial opticalmodulation element) in which a specific amplitude and a specific phaseare recorded.

As specific examples of three-dimensional cells having the function ofrecording both amplitude and phase, the above-mentioned U.S. Pat. No.6,618,190 discloses cells, each having a groove formed by hollowing aportion, of an area that is in accordance with a specific amplitude, byjust a depth that is in accordance with a specific phase, and cells,each having a convex part formed by protruding a portion, of an areathat is in accordance with a specific amplitude, by just a height thatis in accordance with a specific phase. An optical element comprising aset of three-dimensional cells having such characteristic shapes can bemanufactured by a manufacturing process using an electron beam drawingdevice, etc., and thus has the merit of being suited for massproduction.

However, with the optical elements using three dimensional cells thatare disclosed as embodiments in the above-mentioned U.S. Pat. No.6,618,190, noise components become mixed in during reconstruction andclear reconstruction results thus cannot be obtained necessarily. Thisis because a part of the incident light that is provided as illuminationlight in the reconstruction process or a part of the reflected light ofthis incident light is observed as 0th-order diffraction light. Inparticular, when such an optical element that gives rise to such0th-order diffraction light is used in combination with a lens, the0th-order diffraction light becomes converged at the focal pointposition of the lens and cannot be neglected in terms of practical use.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide an opticalelement that can function as a complex amplitude type spatial opticalmodulator in which generation of 0th-order diffraction light is reducedas much as possible.

(1) The first feature of the present invention resides in an opticalelement comprising a set of a plurality of three-dimensional cells:

wherein an individual cell is made of a light transmitting material andhas a specific amplitude and a specific phase defined therein;

a first region, comprising a portion with an area that is in accordancewith the specific amplitude defined in the individual cell, and a secondregion, comprising a portion except the first region, are defined on anupper surface of the individual cell, the first region on the uppersurface of the individual cell being formed by a bottom surface of agroove, having a depth that is in accordance with the specific phasedefined in the individual cell, and a light blocking layer being formedon the second region on the upper surface of the individual cell; and

the individual cell has a specific optical characteristic such that whenpredetermined incident light is provided from the upper surface or alower surface of the cell, transmission emitted light, with whichamplitude and phase of the incident light have been changed inaccordance with the specific amplitude and the specific phase defined inthe cell, is obtained from the lower surface or the upper surface of thecell.

(2) The second feature of the present invention resides in an opticalelement comprising a set of a plurality of three-dimensional cells:

wherein an individual cell has a specific amplitude and a specific phasedefined therein;

a first region, comprising a portion with an area that is in accordancewith the specific amplitude defined in the individual cell, and a secondregion, comprising a portion except the first region, are defined on anupper surface of the individual cell, the first region on the uppersurface of the individual cell being formed by a bottom surface of agroove, having a depth that is in accordance with the specific phasedefined in the individual cell, the bottom surface of the groove being areflecting surface and a light absorbing layer being formed on thesecond region on the upper surface of the individual cell; and

the individual cell has a specific optical characteristic such that whenpredetermined incident light is provided from the upper surface of thecell, reflection emitted light, with which amplitude and phase of theincident light have been changed in accordance with the specificamplitude and the specific phase defined in the cell, is obtained fromthe upper surface of the cell.

(3) The third feature of the present invention resides in an opticalelement comprising a set of a plurality of three-dimensional cells:

wherein an individual cell is made of a light transmitting material andhas a specific amplitude and a specific phase defined therein;

a first region, comprising a portion with an area that is in accordancewith the specific amplitude defined in the individual cell, and a secondregion, comprising a portion except the first region, are defined on anupper surface of the individual cell, the first region on the uppersurface of the individual cell being formed by a bottom surface of agroove, having a depth that is in accordance with the specific phasedefined in the individual cell, a light absorbing layer being formed onthe second region on the upper surface of the individual cell, and alight reflecting layer being formed on a bottom surface of theindividual cell; and

the individual cell has a specific optical characteristic such that whenpredetermined incident light is provided from the upper surface of thecell, reflection emitted light, with which amplitude and phase of theincident light have been changed in accordance with the specificamplitude and the specific phase defined in the cell, is obtained fromthe upper surface of the cell.

(4) The fourth feature of the present invention resides in an opticalelement comprising a set of a plurality of three-dimensional cells:

wherein an individual cell is made of a light transmitting material andhas a specific amplitude and a specific phase defined therein;

a first region, comprising a portion with an area that is in accordancewith the specific amplitude defined in the individual cell, and a secondregion, comprising a portion except the first region, are defined on anupper surface of the individual cell, the first region on the uppersurface of the individual cell being formed by a bottom surface of agroove, having a depth that is in accordance with the specific phasedefined in the individual cell, a light absorbing layer being formed onthe second region on the upper surface of the individual cell, and alight reflecting layer being formed on the first region on the uppersurface of the individual cell; and

the individual cell has a specific optical characteristic such that whenpredetermined incident light is provided from a lower surface of thecell, reflection emitted light, with which amplitude and phase of theincident light have been changed in accordance with the specificamplitude and the specific phase defined in the cell, is obtained fromthe lower surface of the cell.

(5) The fifth feature of the present invention resides in an opticalelement comprising a set of a plurality of three-dimensional cells:

wherein an individual cell is made of a light transmitting material andhas a specific amplitude and a specific phase defined therein;

a first region, comprising a portion with an area that is in accordancewith the specific amplitude defined in the individual cell, and a secondregion, comprising a portion except the first region, are defined on anupper surface of the individual cell, the first region on the uppersurface of the individual cell being formed by a convex part, having aheight that is in accordance with the specific phase defined in theindividual cell, and a light blocking layer being formed on the secondregion on the upper surface of the individual cell; and

the individual cell has a specific optical characteristic such that whenpredetermined incident light is provided from the upper surface or alower surface of the cell, transmission emitted light, with whichamplitude and phase of the incident light have been changed inaccordance with the specific amplitude and the specific phase defined inthe cell, is obtained from the lower surface or the upper surface of thecell.

(6) The sixth feature of the present invention resides in an opticalelement comprising a set of a plurality of three-dimensional cells:

wherein an individual cell has a specific amplitude and a specific phasedefined therein;

a first region, comprising a portion with an area that is in accordancewith the specific amplitude defined in the individual cell, and a secondregion, comprising a portion except the first region, are defined on anupper surface of the individual cell, the first region on the uppersurface of the individual cell being formed by a convex part, having aheight that is in accordance with the specific phase defined in theindividual cell, a top surface of the convex part being a reflectingsurface and a light absorbing layer being formed on the second region onthe upper surface of the individual cell; and

the individual cell has a specific optical characteristic such that whenpredetermined incident light is provided from the upper surface of thecell, reflection emitted light, with which amplitude and phase of theincident light have been changed in accordance with the specificamplitude and the specific phase defined in the cell, is obtained fromthe upper surface of the cell.

(7) The seventh feature of the present invention resides in an opticalelement comprising a set of a plurality of three-dimensional cells:

wherein an individual cell is made of a light transmitting material andhas a specific amplitude and a specific phase defined therein;

a first region, comprising a portion with an area that is in accordancewith the specific amplitude defined in the individual cell, and a secondregion, comprising a portion except the first region, are defined on anupper surface of the individual cell, the first region on the uppersurface of the individual cell being formed by a convex part, having aheight that is in accordance with the specific phase defined in theindividual cell, a light absorbing layer being formed on the secondregion on the upper surface of the individual cell, and a lightreflecting layer being formed on a bottom surface of the individualcell; and

the individual cell has a specific optical characteristic such that whenpredetermined incident light is provided from the upper surface of thecell, reflection emitted light, with which amplitude and phase of theincident light have been changed in accordance with the specificamplitude and the specific phase defined in the cell, is obtained fromthe upper surface of the cell.

(8) The eighth feature of the present invention resides in an opticalelement comprising a set of a plurality of three-dimensional cells:

wherein an individual cell is made of a light transmitting material andhas a specific amplitude and a specific phase defined therein;

a first region, comprising a portion with an area that is in accordancewith the specific amplitude defined in the individual cell, and a secondregion, comprising a portion except the first region, are defined on anupper surface of the individual cell, the first region on the uppersurface of the individual cell being formed by a convex part, having aheight that is in accordance with the specific phase defined in theindividual cell, a light absorbing layer being formed on the secondregion on the upper surface of the individual cell, and a lightreflecting layer being formed on the first region on the upper surfaceof the individual cell; and

the individual cell has a specific optical characteristic such that whenpredetermined incident light is provided from a lower surface of thecell, reflection emitted light, with which amplitude and phase of theincident light have been changed in accordance with the specificamplitude and the specific phase defined in the cell, is obtained fromthe lower surface of the cell.

(9) The ninth feature of the present invention resides in an opticalelement having any one of the first to the eighth features mentionedabove, wherein:

an individual cell is arranged by forming, on a base having a firstrectangular parallelepiped shape, a groove with a second rectangularparallelepiped shape that is smaller than the first rectangularparallelepiped shape.

(10) The tenth feature of the present invention resides in an opticalelement having the ninth feature mentioned above, wherein:

individual cells are aligned in a form of a two-dimensional matrix withrespective upper surfaces being directed upward.

(11) The eleventh feature of the present invention resides in an opticalelement having any one of the first to the tenth features mentionedabove, wherein:

a complex amplitude distribution of object light from an object image isrecorded so that the object image is reconstructed upon observation froma predetermined viewing point position thus to use the optical elementas a hologram.

According to an optical element of the present invention, as forming alight blocking layer or a light absorbing layer on a part, which hasnothing to do with generation of reconstructing light, of respectivethree-dimensional cells functioning as a complex amplitude type spatialoptical modulator, generation of 0th-order diffraction light can bereduced.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view showing general holography for opticallyrecording an object image as interference fringes by use of referencelight.

FIG. 2 is a perspective view showing the amplitude and phase of objectlight that has reached a representative point P(x, y) on a recordingsurface 20 when a point light source O and the recording surface 20 aredefined.

FIG. 3 is a perspective view showing the complex amplitude of objectlight at the position of the representative point P(x, y) when theobject light emitted from each point light source on an object image 10has reached the representative point P(x, y) on the recording surface20.

FIG. 4 shows the calculation of an amplitude A (x, y) and a phase θ(x,y) on the basis of a complex amplitude shown by a coordinate point Q ona complex coordinate plane.

FIG. 5 is a perspective view showing one example of a three-dimensionalvirtual cell set 30 defined to record the object image 10.

FIG. 6 shows the function of the amplitude modulation and phasemodulation of a three-dimensional cell C(x, y) used in the presentinvention.

FIG. 7 shows one example of 16 kinds of physical cells different intransmittance and in refractive index that are to be the constituentparts of an optical element according to the present invention.

FIG. 8 is a perspective view showing one example of the structure of aphysical cell C(x, y) considered most suitable for use in the presentinvention.

FIG. 9 is a front view for explaining a reason why amplitude informationis recorded as a width G1 of a groove G(x, y) and phase information isrecorded as a depth G2 of the groove G(x, y) when the physical cell C(x,y) shown in FIG. 8 is used as a transmission type cell.

FIG. 10 is a front view for explaining a reason why amplitudeinformation is recorded as the width G1 of the groove G(x, y) and phaseinformation is recorded as the depth G2 of the groove G(x, y) when thephysical cell C(x, y) shown in FIG. 8 is used as a reflection type cell.

FIG. 11 is a perspective view showing an example in which seven kinds ofgroove widths and four kinds of depths are determined so that 28 kindsof physical cells in total are prepared in the structure of the physicalcell C(x, y) shown in FIG. 8.

FIG. 12 shows the relationship between the refractive index and thegroove depth of each part for the transmission type cell C(x, y).

FIG. 13 shows the relationship between the refractive index and thegroove depth of each part for the reflection type cell C(x, y).

FIG. 14 is a side view showing a basic form in which reconstructingillumination light is projected from a normal direction onto the opticalelement which is a basic form of the present invention, and an objectimage recorded as a hologram is observed from the normal direction.

FIG. 15 is a side view showing a form in which reconstructingillumination light is projected from an oblique direction onto theoptical element which is a basic form of the present invention, and anobject image recorded as a hologram is observed from the normaldirection.

FIG. 16 is a side view showing a form in which reconstructingillumination light is projected from the normal direction onto theoptical element which is a basic form of the present invention, and anobject image recorded as a hologram is observed from the obliquedirection.

FIG. 17 is a side view showing a principle according to which specificphase is subjected to corrective processing in order to make an opticalelement that corresponds to a reconstructing environment shown in FIG.15.

FIG. 18 is a side view showing a principle according to which specificphase is subjected to corrective processing in order to make an opticalelement that corresponds to a reconstructing environment shown in FIG.16.

FIG. 19 is a perspective view showing a technique for making an opticalelement that corresponds to a reconstructing environment in which whitereconstructing illumination light is used.

FIG. 20 is a perspective view showing an example in whichthree-dimensional cells are arranged like a one-dimensional matrix so asto construct a three-dimensional virtual cell set 30.

FIG. 21 is a perspective view of an example of the structure of aphysical cell C1(x, y) of a first groove type embodiment of the presentinvention.

FIG. 22 is a sectional view of the physical cell shown in FIG. 21(hatching of the main body portion of the cell is omitted).

FIG. 23 is a perspective view of an example of the structure of aphysical cell C2(x, y) of a second groove type embodiment of the presentinvention.

FIG. 24 is a sectional view of the physical cell shown in FIG. 23(hatching of the main body portion of the cell is omitted).

FIG. 25 is a perspective view of an example of the structure of aphysical cell C3(x, y) of a third groove type embodiment of the presentinvention.

FIG. 26 is a sectional view of the physical cell shown in FIG. 25(hatching of the main body portion of the cell is omitted).

FIG. 27 is a sectional view of a modification example of the physicalcell shown in FIG. 26 (hatching of the main body portion of the cell isomitted).

FIG. 28 is a sectional view of another modification example of thephysical cell shown in FIG. 26 (hatching of the main body portion of thecell is omitted).

FIG. 29 is a perspective view of an example of the structure of aphysical cell CC(x, y) of a fourth groove type embodiment of the presentinvention.

FIG. 30 is a sectional view of the physical cell shown in FIG. 29.

FIG. 31 is a perspective view of an example of the structure of aphysical cell C6(x, y) of a first convex type embodiment of the presentinvention.

FIG. 32 is a sectional view of the physical cell shown in FIG. 31(hatching of the main body portion of the cell is omitted).

FIG. 33 is a sectional view of an example of the structure of a physicalcell C7(x, y) of a second convex type embodiment of the presentinvention (hatching of the main body portion of the cell is omitted).

FIG. 34 is a sectional view of an example of the structure of a physicalcell C8(x, y) of a third convex type embodiment of the present invention(hatching of the main body portion of the cell is omitted).

FIG. 35 is a sectional view of a simple model of an optical element bythe present invention.

FIGS. 36A to 36C are sectional views of the stages of the first half ofa process of manufacturing the model shown in FIG. 35.

FIGS. 37A to 37D are sectional views of the stages of the latter half ofthe process of manufacturing the model shown in FIG. 35.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be hereinafter described on the basis of theembodiments shown in the figures. Incidentally, the present invention isan improved version of the former invention described in theabove-mentioned U.S. Pat. No. 6,618,190 (hereinafter, this formerinvention is referred to as the basic invention). Therefore, first, thebasic invention is described in § 1 to § 5 and then improved parts ofthe present invention are described in § 6 and § 7.

<<<§ 1. Basic Principle of the Basic Invention>>>

FIG. 1 is a perspective view that shows general holography in which anobject image is optically recorded as interference fringes by use ofreference light. When a stereoscopic image of an object 10 is recordedonto a recording medium 20, the object 10 is illuminated with light(normally, with a laser beam) having the same wavelength as referencelight R, and interference fringes formed by object light from the object10 and the reference light R on the recording medium 20 are recorded.Herein, if an XY coordinate system is defined on the recording medium20, and attention is paid to an arbitrary point P(x, y) located atcoordinates (x, y), the amplitude intensity of a composite waveresulting from interference between each object light from each pointO(1), O(2), . . . , O(k), . . . , O(K) located on the object 10 and thereference light R will be recorded onto the point P(x, y). Likewise, theamplitude intensity of the composite wave resulting from theinterference between the object light from each point and the referencelight R will be recorded onto another point P(x′,y′) on the recordingmedium 20. However, since a difference in the propagation distance oflight exists, the amplitude intensity recorded onto the point P(x, y)and the amplitude intensity recorded onto the point P(x′,y′) aredifferent from each other. As a result, an amplitude intensitydistribution is recorded onto the recording medium 20, and the amplitudeand phase of the object light are expressed by this amplitude intensitydistribution. When reconstructed, reconstructing illumination lighthaving the same wavelength as the reference light R is projected fromthe same direction as that of the reference light R (or, alternatively,from a direction that has a plane symmetry with respect to the recordingmedium 20), and thus a stereoscopic reconstructed image of the object 10is obtained.

In order to record interference fringes onto the recording medium 20according to an optical method, a photosensitive material is used as therecording medium 20, and interference fringes are recorded as a lightand dark pattern on the recording medium 20. On the other hand, if thecomputer generated hologram method is used, a phenomenon occurring inthe optical system shown in FIG. 1 requires simulation on a computer.Specifically, the object image 10 and the recording surface 20 aredefined in a virtual three-dimensional space on the computer instead ofthe real object 10 or the real recording medium 20, and many point lightsources O(1), O(2), . . . , O(k), . . . , O(K) are defined on the objectimage 10. Further, object light (i.e., spherical wave) with apredetermined wavelength, amplitude, and phase is defined for each pointlight source, and reference light with the same wavelength as the objectlight is defined. On the other hand, many representative points P(x, y)are defined on the recording surface 20, and the amplitude intensity ofa composite wave of both the object light and the reference light thatreach the position of each representative point is calculated. Since anamplitude intensity distribution (i.e., interference fringes) isobtained on the recording surface 20 by computation, a physical hologramrecording medium can be formed if the amplitude intensity distributionis recorded onto the physical recording medium in the form of alight/dark distribution or as a concave/convex distribution.

In fact, the interference fringes are not necessarily required to berecorded by using the reference light R if the computer-generatedhologram method is used. It is also possible to record the object lightfrom the object image 10 directly onto the recording surface 20. In moredetail, when a hologram is optically generated, it is necessary togenerate an interference wave on the recording medium 20 made of aphotosensitive material during a fixed period of time needed forexposure and to record this wave as interference fringes. Therefore, itis necessary to generate an interference wave that turns to a standingwave by use of reference light. However, if the computer-generatedhologram method is used, the state of the wave at a certain moment thatexists on the recording surface 20 can be observed in such a way as if alapse in time is stopped, and this wave can be recorded. In other words,the amplitude and phase of the object light at the position of eachrepresentative point on the recording surface 20 at a predeterminedstandard time can be obtained by calculation. In the embodiment of thebasic invention described in the above-mentioned U.S. Pat. No.6,618,190, this advantage in a computer-generated hologram is employed,and the method for directly recording the amplitude and phase of theobject light is used without using the method for recording the objectlight as interference fringes resulting from cooperation with thereference light.

Now let us consider how the amplitude and phase of the object light thathas reached the representative point P(x, y) on the recording surface 20are calculated when the point light source O and the recording surface20 are defined as shown in, for example, the perspective view of FIG. 2.Generally, a wave motion in consideration of the amplitude and the phaseis expressed by the following function of complex variable (i is animaginary unit):A cos θ+i A sin θHerein, A is a parameter showing the amplitude, and θ is a parametershowing the phase. Accordingly, if object light emitted from a pointlight source O is defined by the function A cos θ+i A sin θ, the objectlight at the position of a representative point P(x, y) is expressed bythe following function of the complex variable:A/r cos(θ+2πr/λ)+i A/r sin(θ+2πr/λ)Herein, r is a distance between the point light source O and therepresentative point P(x, y), and λ is a wavelength of the object light.The amplitude of the object light attenuates as the distance r becomesgreater, and the phase depends on the distance r and the wavelength λ.This function does not have variables that indicate time. The reason isthat this function is an expression showing the momentary state of awave observed when a lapse in time is stopped at a predeterminedstandard time as described above.

Accordingly, in order to record information for the object image 10 ontothe recording surface 20, many point light sources O(1), O(2), . . . ,O(k), . . . , O(K) are defined on the object image 10 as shown in theperspective view of FIG. 3, and then the amplitude and phase of acomposite wave of the object light emitted from each point light sourceare calculated at the position of each representative point on therecording surface 20, and the calculation result is recorded by acertain method. Let us now suppose that K point light sources in totalare defined on the object image 10, and the object light emitted fromthe k-th (“-th” is a suffix indicating an ordinal number) point lightsource O(k) is expressed by the following function of the complexvariable as shown in FIG. 3:Ak cos θk+i Ak sin θkIf the object image 10 is constructed of a set of pixels each of whichhas a predetermined gradation value (concentration value), the parameterAk showing the amplitude is fixed in accordance with the gradation valueof a pixel which exists at the position of the point light source O(k).The phase θk is allowed to be defined generally as θk=0. However, it isalso possible to create such a setting as to emit object light raysdifferent in phase from each part of the object image 10 if necessary.When the object light expressed by the above function can be defined foreach of all the K point light sources, the composite wave of all the Kobject light at the position of an arbitrary representative point P(x,y) on the recording surface 20 is expressed by the following function ofthe complex variable as shown in FIG. 3:

$\sum\limits_{{k = 1},K}\left( {{{Ak}\text{/}{rk}\mspace{11mu}{\cos\left( {{\theta\; k} + {2\pi\;{rk}\text{/}\lambda}} \right)}} + {i\mspace{11mu}{Ak}\text{/}{rk}\mspace{11mu}{\sin\left( {{\theta\mspace{11mu} k} + {2\pi\mspace{11mu}{rk}\text{/}\lambda}} \right)}}} \right)$Herein, rk is the distance between the k-th point light source O(k) andthe representative point P(x, y). The above function corresponds to anexpression that is used when the object image 10 is reconstructed at theback of the recording medium. When the object image 10 is reconstructedto rise to the front side of the recording medium, the function of thecomplex variable is merely calculated according to the followingexpression (note that the reference character in the term of the phaseis negative):

$\sum\limits_{{k = 1},K}\left( {{{Ak}\text{/}{rk}\mspace{11mu}{\cos\left( {{\theta\; k} - {2\pi\;{rk}\text{/}\lambda}} \right)}} + {i\mspace{11mu}{Ak}\text{/}{rk}\mspace{11mu}{\sin\left( {{\theta\mspace{11mu} k} - {2\pi\mspace{11mu}{rk}\text{/}\lambda}} \right)}}} \right)$

Therefore, the function of the complex variable in consideration of bothsituations is as follows:

$\sum\limits_{{k = 1},K}\left( {{{Ak}\text{/}{rk}\mspace{11mu}{\cos\left( {{\theta\; k} \pm {2\pi\;{rk}\text{/}\lambda}} \right)}} + {i\mspace{11mu}{Ak}\text{/}{rk}\mspace{11mu}{\sin\left( {{\theta\mspace{11mu} k} \pm {2\pi\mspace{11mu}{rk}\text{/}\lambda}} \right)}}} \right)$If the form of Rxy+iIxy is taken under the condition that the realnumber part of this function is Rxy and the imaginary number partthereof is Ixy, the complex amplitude (i.e., amplitude in considerationof the phase) at the position of the representative point P(x, y) ofthis composite wave is shown by a coordinate point Q on the complexcoordinate plane as shown in FIG. 4. After all, the amplitude of thecomposite wave of the object light at the representative point P(x, y)is given by the distance A(x, y) between the origin O and the coordinatepoint Q on the coordinate plane shown in FIG. 4, and the phase is givenby the angle θ(x, y) between the vector OQ and the real number axis.

Thus, the amplitude A(x, y) and phase θ(x, y) of the composite wave ofthe object light at the position of the arbitrary representative pointP(x, y) defined on the recording surface 20 is obtained by computation.Accordingly, the complex amplitude distribution (i.e., distribution ofthe amplitude and phase of the object light-composite wave) of theobject light emitted from the object image 10 is obtained on therecording surface 20. As a result, the object image 10 can be recordedas a hologram if the complex-amplitude distribution obtained in this wayis recorded on a physical recording medium in some way so that the wavefront of the object light is to be reconstructed and then predeterminedreconstructing illumination light is given.

In order to record a complex amplitude distribution of object lightemitted from the object image 10 onto the recording surface 20, thebasic invention adopts a method for using three-dimensional cells. Thefollowing procedure should be carried out to record a complex amplitudedistribution by use of three-dimensional cells and record the objectimage 10 as a hologram. First, a three-dimensional virtual cell set 30is defined at the position of the recording surface 20 as shown in FIG.5, for example. The three-dimensional virtual cell set 30 is constructedby vertically and horizontally arranging block-like virtual cells eachof which has a predetermined size so as to place the cellstwo-dimensionally. Thereafter, the representative point of each virtualcell is defined. The position of the representative point may be onearbitrary point in the cell. In this case, the representative point ofthe cell is defined at the position of the center point on the frontsurface of the cell (i.e., surface facing the object image 10). Forexample, if an XY coordinate system is defined on the front surface ofthe three-dimensional virtual cell set 30 (i.e., on the surface facingthe object image 10), and a virtual cell having the representative pointP(x, y) located at the position of coordinates (x, y) in this coordinatesystem is called a virtual cell C(x, y), the representative point P(x,y) will occupy the center point of the front surface of this virtualcell C(x, y).

On the other hand, the object image 10 is defined as a set of pointlight sources. In the example of FIG. 5, the object image 10 is definedas a set of K point light sources O(1), O(2), . . . , O(k), . . . ,O(K). Object light having predetermined amplitude and phase is emittedfrom each point light source, and a composite wave of these object lightrays reaches the representative point P(x, y). The complex amplitude ofthis composite wave can be calculated according to the above-mentionedexpressions and can be shown as a coordinate point Q on the complexcoordinate plane shown in FIG. 4, and, based on this coordinate point Q,the amplitude A(x, y) and phase θ(x, y) are obtained, as describedabove. Herein, the amplitude A(x, y) and phase θ(x, y) obtained for therepresentative point P(x, y) will be called a specific amplitude A(x, y)and a specific phase θ(x, y) for the virtual cell C(x, y) including therepresentative point P(x, y).

The above-mentioned procedure is practically carried out as arithmeticprocessing by use of a computer. Accordingly, concerning each of all thevirtual cells that make up the three-dimensional virtual cell set 30, aspecific amplitude and a specific phase can be obtained by thisarithmetic processing. Therefore, an optical element (i.e., a hologramrecording medium in which the object image 10 is recorded) that is madeup of a set of three-dimensional physical cells can be formed byreplacing these virtual cells with real physical cells, respectively.Herein, the physical cell to be replaced with the virtual cell must haveoptical properties by which the amplitude and phase of incidence lightcan be modulated in accordance with the specific amplitude and specificphase defined in the virtual cell. In other words, when predeterminedincidence light is given, the replaced individual physical cell musthave the specific optical properties of having a function to generateemission light by changing the amplitude and phase of the incidencelight in accordance with the specific amplitude and specific phase thathave been defined in the virtual cell before replacement.

When predetermined reconstructing illumination light (ideally, a planewave of monochromatic light with the same wavelength as the wavelength λof the object light used in the above-mentioned arithmetic processing)is projected onto the optical element made up of a set of physical cellshaving the specific optical properties, the reconstructing illuminationlight is modulated by the specific amplitude and the specific phase ineach physical cell. Therefore, the original wave front of the objectlight is reconstructed. As a result, the hologram recorded in thisoptical element is reconstructed.

<<<§ 2. Concrete Structure of Physical Cell>>>

Next, the concrete structure of a physical cell used in the basicinvention will be described. A physical cell used in the basic inventiontheoretically is a three-dimensional stereo-cell, and its specificamplitude and its specific phase are defined. Any type of cell can beused if it has such a specific optical property that emission light inwhich the amplitude and phase of predetermined incidence light arechanged in accordance with the specific amplitude and specific phasedefined in the cell can be obtained when the incidence light is given tothe cell. For example, in a case in which an amplitude A(x, y) and aphase θ(x, y) is recorded for a three-dimensional cell C(x, y) shown inFIG. 6, and incidence light Lin whose amplitude is Ain and whose phaseis θin is given to this cell, all that is needed is to obtain emissionlight Lout whose amplitude Aout equals Ain·A(x, y) and whose phase θoutequals θin±θ(x, y). The amplitude Ain of the incidence light undergoesmodulation by the specific amplitude A(x, y) recorded on the cell andchanges into the amplitude Aout, whereas the phase θin of the incidencelight undergoes modulation by the specific phase θ(x, y) recorded on thecell and changes into the phase θout.

One method for modulating the amplitude in the three-dimensional cell isto provide an amplitude-modulating part having transmittance thatcorresponds to the specific amplitude in the cell (the entire cell maybe used as the amplitude-modulating part, or the amplitude-modulatingpart may be provided to a part of the cell). For example, a cellprovided with the amplitude-modulating part whose transmittance is Z %serves as a cell in which the specific amplitude of A(x, y) equal toZ/100 is recorded, and, when incidence light with the amplitude Ainpasses through this cell, it is subjected to amplitude modulation byemission light whose amplitude Aout equals Ain·Z/100. One possiblemethod for setting the transmittance of each three-dimensional cell atan arbitrary value is to, for example, change the content of a coloringagent for each cell.

Another method for modulating the amplitude in the three-dimensionalcell is to provide an amplitude-modulating part having reflectivity thatcorresponds to the specific amplitude in the cell. For example, a cellprovided with the amplitude-modulating part whose reflectivity is Z %serves as a cell in which the specific amplitude of A(x, y) equal toZ/100 is recorded, and, when incidence light with the amplitude Ain isreflected by this amplitude-modulating part and is emitted, it issubjected to amplitude modulation by emission light whose amplitude Aoutequals Ain·Z/100. One possible method for setting the reflectivity ofeach three-dimensional cell at an arbitrary value is to, for example,prepare a reflecting surface in the cell (this reflecting surface servesas the amplitude-modulating part) and set the reflectivity of thereflecting surface at an arbitrary value. More specifically, the ratioof reflected light to scattered light can be adjusted by, for example,changing the surface roughness of the reflecting surface, and thereforethe adjustment of the surface roughness makes it possible to prepare acell having arbitrary reflectivity.

Still another method for modulating the amplitude in thethree-dimensional cell is to provide an amplitude-modulating part havingan effective area that corresponds to the specific amplitude in thecell. For example, if it is assumed that the area of all the incidentregion of incidence light is 100%, a cell having an amplitude-modulatingpart constructed such that emission light effective for reconstructingan object image can be obtained only from incidence light that hasstruck a part having a Z % effective area thereof serves as a cell inwhich the specific amplitude of A(x, y)=Z/100 is recorded. That is, evenif incidence light having the amplitude Ain strikes theamplitude-modulating part, only Z % of the light goes out as effectiveemission light, and therefore it is subjected to amplitude modulation byemission light having the amplitude of Aout=Ain·Z/100. One possiblemethod for obtaining effective emission light only from a region havingsuch a specific effective area is to use a cell having a physicalconcave/convex structure. The present invention relates to an opticalelement using a three-dimensional cells having such a structure and aconcrete example thereof will be described in § 3.

On the other hand, one method for modulating the phase in thethree-dimensional cell is to provide a phase-modulating part having arefractive index that corresponds to the specific phase in the cell (theentire cell can be used as the phase-modulating part, or thephase-modulating part can be provided to a part of the cell). Forexample, even if incidence light with the same phase is given, adifference in the phase of emission light arises between a cell providedwith the phase-modulating part made of a material whose refractive indexis n1 and a cell provided with the phase-modulating part made of amaterial whose refractive index is n2. Therefore, arbitrary phasemodulation can be applied to the incidence light by constructing thecell made of various materials with different refractive indexes.

Another method for modulating the phase in the three-dimensional cell isto provide a phase-modulating part having an optical path length thatcorresponds to the specific phase in the cell (the entire cell can beused as the phase-modulating part, or the phase-modulating part can beprovided to a part of the cell). For example, even if the cell has aphase-modulating part made of the same material whose refractive indexis n, a difference in the phase of each emission light will arise if theoptical path length of the phase-modulating part is different regardlessof the fact that incidence light with the same phase is given. Forexample, if the optical path length of the phase-modulating partprovided in a first cell is L, and the optical path length of thephase-modulating part provided in a second cell is 2L, the distance bywhich emission light emitted from the second cell travels through thematerial whose refractive index is n is twice as long as in the case ofemission light emitted from the first cell even if incidence light withthe same phase is given. Therefore, such a great phase differencearises. A method for realizing a phase-modulating part with an arbitraryoptical path length is to still use a cell having a physicalconcave/convex structure. A concrete example thereof will be describedin § 3.

A three-dimensional cell having an amplitude modulating function basedon a specific amplitude or a three-dimensional cell having a phasemodulating function based on a specific phase can be realized by some ofthe methods described above, and an optical element according to thepresent invention can be realized by selecting an arbitrary method fromamong the amplitude modulating methods and the phase modulating methodsmentioned above. For example, if a method in which anamplitude-modulating part with transmittance that corresponds to aspecific amplitude is provided in the cell is employed as the amplitudemodulating method, and a method in which a phase-modulating part with arefractive index that corresponds to a specific phase is provided in thecell is employed as the phase modulating method, and the entire cell isused as the amplitude-modulating part and as the phase-modulating part,an optical element can be formed by selectively arranging 16 kinds ofphysical cells shown in the table of FIG. 7. The horizontal axis of thistable indicates amplitude A, and the vertical axis thereof indicatesphase θ. The amplitude A and the phase θ are each divided into fourranges.

Herein, the cells (i.e., cells of the first column in the table)depicted in a range in which the amplitude A corresponds to “0-25%” areones that are each made of a material whose transmittance is very low,the cells (i.e., cells of the second column in the table) depicted in arange in which the amplitude A corresponds to “25-50%” are ones that areeach made of a material whose transmittance is slightly low, the cells(i.e., cells of the third column in the table) depicted in a range inwhich the amplitude A corresponds to “50-75%” are ones that are eachmade of a material whose transmittance is slightly high, and the cells(i.e., cells of the fourth column in the table) depicted in a range inwhich the amplitude A corresponds to “75-100%” are ones that are eachmade of a material whose transmittance is very high. On the other hand,the cells (i.e., cells of the first row in the table) depicted in arange in which the phase θ corresponds to “0-π/2” are ones that are eachmade of a material whose refractive index n1 is very close to that ofair, the cells (i.e., cells of the second row in the table) depicted ina range in which the phase θ corresponds to “π/2-π” are ones that areeach made of a material whose refractive index n2 is slightly greaterthan that of air, the cells (i.e., cells of the third row in the table)depicted in a range in which the phase θ corresponds to “π-3π/2” areones that are each made of a material whose refractive index n3 is muchgreater than that of air, and the cells (i.e., cells of the fourth rowin the table) depicted in a range in which the phase θ corresponds to“3π/2-2π” are ones that are each made of a material whose refractiveindex n4 is very much greater than that of air.

In the example of FIG. 7, sixteen cells in total with four kinds oftransmittances and four kinds of refractive indexes are prepared asdescribed above. A desirable way of recording the amplitude and phase inthe cell with higher accuracy is to set the transmittance steps and therefractive-index steps in more detail and prepare even more kinds ofcells. What is needed to replace the virtual cells by use of thesesixteen kinds of physical cells is to select a physical cell that hasoptical properties closest in the optical properties needed to carry outmodulation based on the specific amplitude and the specific phasedefined in each virtual cell.

<<<§ 3. Practical Structure of Physical Cell>>>

If physical cells used in the basic invention are cells that have afunction to modulate incidence light in accordance with a specificamplitude and a specific phase as described above, any kind of cellstructure is allowed in principle to embody the basic invention. FIG. 7shows an example in which the modulation according to a specificamplitude is controlled by the transmittance, and the modulationaccording to a specific phase is controlled by the refractive index.Theoretically, many methods exist to modulate the amplitude or the phaseas described above. However, from the viewpoint of industrial massproduction, all the methods are not necessarily practical. In order toreconstruct an object image that has a certain degree of resolution byusing the optical element based on the principle of the basic invention,the size of each three-dimensional cell must be determined to be lessthan a criterion (roughly speaking, when the size of a cell exceeds 100μm, it is difficult to reconstruct a satisfactorily discernible objectimage). Therefore, it is need to two-dimensionally arrange small cellsas a component if sixteen kinds of physical cells shown in FIG. 7 arecombined to form an optical element, and, additionally, there is a needto dispose a specific cell of the sixteen kinds of cells at a specificposition. From this fact, it can be found that the method forconstructing the optical element using the physical cells shown in FIG.7 is unsuitable for industrial mass production.

As a method in which amplitude information and phase information can begiven to a single physical cell and an optical element suitable forindustrial mass production is constructed with a set of such physicalcells, a unique method is proposed in the above-mentioned U.S. Pat. No.6,618,190 for giving a concave/convex structure to each physical cell,then recording amplitude information as the area of this concave/convexstructure part, and recording phase information as a level difference(i.e., depth of a concave part or height of a convex part) in theconcave/convex structure part.

FIG. 8 is a perspective view showing an example of the structure of aphysical cell C(x, y) that can be regarded as most suitable for use inthe basic invention. As shown in the figure, this three-dimensionalphysical cell is constituted of a base having a rectangular solid blockshape. On an upper surface of the base, a groove G(x, y) is formed whichhas another rectangular solid block shape smaller than the former solidblock. As mentioned later, it is possible to constitute a physical cellhaving a same function by providing a convex part B(x, y) having arectangular solid block shape instead of providing a groove G(x, y).

In this example, the size of the physical cell C(x, y), C1=0.6 μm,C2=0.25 μm, and C3=0.25 μm, and the size of the groove G(x, y), G1=0.2μm, G2=0.05 μm, and G3=C3=0.25 μm are shown in the figure. The use ofthe thus constructed physical cell C(x, y) makes it possible to recordthe amplitude information as a value of the lateral width G1 of thegroove G(x, y) and record the phase information as a value of the depthG2 of the groove G(x, y). In other words, when a virtual cell in which aspecific amplitude and a specific phase are defined is replaced with thethus constructed physical cell, the replacement is carried out by thephysical cell having the size G1 corresponding to the specific amplitudeand having the size G2 corresponding to the specific phase.

With reference to the front view of FIG. 9, a description will beprovided of the reason why the amplitude information is recorded as thewidth G1 of the groove G(x, y) and the phase information is recorded asthe depth G2 of the groove G(x, y) in the physical cell shown in FIG. 8.Let us now suppose that the physical cell C(x, y) is made of a materialwith the refractive index n2, and the part outside the physical cellC(x, y) is made of a material (e.g., air) with the refractive index n1.In this case, when the optical path length passing through the mediumwith the refractive index n2 is compared between incident light L1 thathas struck vertically the inner surface S1 of the groove G(x, y) andincident light L2 that has struck vertically the outer surface S2 of thegroove G(x, y), it can be found that the optical path length of thelight L1 is shorter than that of the light L2 by the depth G2 of thegroove G(x, y). Therefore, if the refractive indexes n1 and n2 aredifferent from each other, a predetermined phase difference will arisebetween the light L1 and the light L2 emitted from the physical cellC(x, y) as transmission light.

On the other hand, FIG. 10 is a front view showing a case in whichemission light is obtained as reflected light from the physical cellC(x, y). In this example, the upper surface of the physical cell C(x,y), i.e., surfaces S1 and S2 are reflecting surfaces, and the incidentlight L1 that has struck almost vertically the inner surface S1 of thegroove G(x, y) and the incident light L2 that has struck almostvertically the outer surface S2 of the groove G(x, y) are reflected bythe respective surfaces almost vertically and emitted therefrom. At thistime, it can be found that, when the entire optical path length alongthe path of the incidence and reflection is compared, the optical pathlength of the light L1 becomes longer than that of the light L2 bydouble the depth G2 of the groove G(x, y). Therefore, a predeterminedphase difference arises between the light L1 and the light L2 emittedfrom the physical cell C(x, y) as reflected light.

Accordingly, even if the physical cell C(x, y) is a transmission typecell or a reflection type cell, a predetermined phase difference arisesbetween the incident light L1 that has struck the inner surface S1 ofthe groove G(x, y) and the incident light L2 that has struck the outersurface S2 of the groove G(x, y). This phase difference depends on thedepth G2 of the groove G(x, y). Therefore, if only the emission lightobtained on the basis of the incidence light that has struck the innersurface S1 of the groove G(x, y) among the incident light rays that havestruck the upper surface of the physical cell C(x, y) is treated asemission light effective for the reconstruction of the object image 10(in other words, if only the light L1 is treated as emission lighteffective for the reconstruction of the image in FIG. 9 or FIG. 10),emission light L1 effective for the image reconstruction resultantlyundergoes phase-modulation by a specific phase that corresponds to thedepth G2 of the groove G(x, y) in this physical cell C(x, y). Thus, thephase information of the object light can be recorded as the depth G2 ofthe groove G(x, y).

Further, if only the emission light obtained on the basis of theincidence light that has struck the inner surface S1 of the groove G(x,y) is treated as emission light effective for the reconstruction of theobject image 10 as mentioned above, the amplitude information of theobject light can be recorded as the width G1 of the groove G(x, y). Thereason is that the area of the inner surface S1 of the groove G(x, y)enlarges, and the percentage of the emission light effective for thereconstruction of the object image 10 increases as the width G1 of thegroove G(x, y) becomes greater. That is, since the emission light L2shown in FIG. 9 or FIG. 10 does not include any significant phasecomponents, the emission light is merely observed as a noise componentof a so-called background, and is not recognized as light effective forreconstructing a significant image even if the emission light L2 isobserved at a viewing position when reconstructed. By contrast, sincethe emission light L1 includes significant phase components, it isobserved as a signal component effective for image reconstruction. Afterall, the width G1 of the groove G(x, y) becomes a factor for determiningthe ratio of the light L1 observed as a signal component among the lightrays emitted from the physical cell C(x, y), and becomes a parameter forgiving the amplitude information of the signal wave.

Generally, the amplitude information is not expressed by the width G1 ofthe groove G(x, y), but by the area of the inner surface S1 of thegroove G(x, y). In the embodiment shown in FIG. 8, since the length G3of the groove G(x, y) happens to be set to be always equal to the lengthC3 of the physical cell C(x, y), the area of the inner surface S1 of thegroove G(x, y) is proportional to the extent of the width G1. However,the length G3 of the groove G(x, y) does not necessarily need to befixed, and both of the width and the length may be changed so that thearea of the inner surface S1 of the groove G(x, y) has variations.

If a part having an area corresponding to the specific amplitude (i.e.,a part corresponding to the surface S1 of FIG. 8) of the upper surfaceof the block-like physical cell is hollowed by the depth correspondingto the specific phase (i.e., depth corresponding to the dimension G2 ofFIG. 8) so as to form a concave part (i.e., groove G(x, y)) in this way,the amplitude modulation corresponding to the specific amplitude and thephase modulation corresponding to the specific phase can be applied toreconstructing illumination light by the thus constructed physical cell.Even if a convex part, instead of the concave part, is formed on theblock-like physical cell, similar modulation processing can be applied.That is, even if the dimension G2 is set at a negative value, and aprojection instead of the groove is formed on the physical block shownin FIG. 8, it is possible to produce an optical path differencecorresponding to the height of the projection and produce a phasedifference. In other words, if a part having an area corresponding tothe specific amplitude of the upper surface of the block-like physicalcell is protruded by the height corresponding to the specific phase soas to form a convex part, the amplitude modulation corresponding to thespecific amplitude and the phase modulation corresponding to thespecific phase can also be applied to reconstructing illumination lightby the thus constructed physical cell.

The width G1 and depth G2 of the groove can be consecutively changed inthe physical cell C(x, y) having the groove G(x, y) shown in FIG. 8, andtherefore, theoretically, infinite kinds of physical cells can beprepared. The use of the infinite kinds of physical cells makes itpossible to replace the virtual cell with the physical cell having theaccurate groove width G1 corresponding to the specific amplitude and theaccurate depth G2 corresponding to the specific phase that are definedin the virtual cell. However, practically, it is preferable topredetermine α kinds of groove widths and β kinds of depths so as toprepare α×β kinds of physical cells in total and then select a physicalcell closest in necessary optical properties from among the physicalcells. FIG. 11 is a perspective view showing an example in which sevenkinds of groove widths and four kinds of depths are determined so as toprepare 28 kinds of physical cells in total. Each of the 28 kinds ofphysical cells is a block-like physical cell formed as shown in FIG. 8,and, in FIG. 11, the physical cells are arranged in the form of a matrixof four rows and 7 columns.

In FIG. 11, the seven columns of the matrix indicate the variation ofamplitude A, and the four rows thereof indicate the variation of phaseθ. For example, the cell located at column W1 is a cell corresponding tothe minimum value of amplitude A, wherein groove Width G1=0, i.e., agroove G is not formed at all. Rightward, i.e., toward columns W2 to W7,the cells correspond to greater amplitude A, and the groove width G1thereof gradually becomes greater. The cell located at column W7 is acell corresponding to the maximum value of amplitude A, wherein groovewidth G1=cell width C1, i.e., the entire surface thereof is hollowed.Further, when attention is paid to the rows of the matrix of FIG. 11,the cell located at row V1, for example, is a cell corresponding to theminimum value of phase θ, wherein groove depth G2=0, i.e., a groove G isnot formed at all. Downward, i.e., toward rows V2 to V4, the cellscorrespond to greater phase θ, and the groove depth G2 thereof graduallybecomes greater.

<<<§ 4. Optical Element Manufacturing Method by Use of PracticalPhysical Cells>>>

Now, a description will be provided of a concrete method formanufacturing an optical element (hologram-recording medium) where anobject image 10 is recorded by use of 28 kinds of physical cells shownin FIG. 11. First, as shown in FIG. 5, the object image 10 formed by aset of point light sources and a three-dimensional virtual cell set 30are defined by use of a computer. Herein, respective virtual cells thatmake up the three-dimensional virtual cell set 30 are block-like cells(at this moment, a groove has not yet been formed) as shown in FIG. 8,and the three-dimensional virtual cell set 30 is formed by arranging thecells two-dimensionally and with equal pitches vertically andhorizontally. The dimension of one virtual cell should be, for example,C1=0.6 μm, C2=0.25 μm, and C3=0.25 μm or so. In this case, if thelateral pitch of the cell is 0.6 μm, and the longitudinal pitch is 0.25μm, the cells can be disposed without any gap. Of course, thedimensional value of each cell shown here is one example, and, inpractice, it is possible to set it at an arbitrary dimension ifnecessary. However, as the cell dimension becomes greater, the visualangle by which a reconstructed image of an object is obtained isnarrowed, and the resolution of the object is lowered proportionately.Reversely, as the cell dimension becomes smaller, the processing offorming a concave/convex structure of the physical cell technicallybecomes difficult. In consideration of the arithmetic processing or theconvenience of the processing of the physical cells, it is preferable todispose the cells with predetermined equal pitches vertically andhorizontally though they do not necessarily need to be disposed withequal pitches. Further, the cells are not necessarily need to bedisposed in an XY-rectangular coordinates, and it is possible to disposethem in an rθ-polar coordinates.

After the definition of the object image 10 and the definition of thethree-dimensional virtual cell set 30 are completed, a representativepoint is defined in each virtual cell, and then the complex amplitude ofthe composite wave of each object light that has reached eachrepresentative point is calculated as described in § 2, and a specificamplitude and a specific phase are defined for each virtual cell.Thereafter, each virtual cell is replaced with any one of the 28 kindsof physical cells shown in FIG. 11 (in other words, it is replaced witha physical cell closest in optical properties needed for modulationaccording to the specific amplitude and the specific phase defined ineach individual virtual cell), and an optical element is formed as a setof physical cells. At this time, the groove-forming surface of eachphysical cell (in the case of the physical cell shown in FIG. 8 or FIG.11, the upper surface) is designed to face the front surface (i.e., thesurface facing the object image 10) of the three-dimensional virtualcell set 30 shown in FIG. 5.

In fact, the replacement of the virtual cell with the physical cell iscarried out as the processing of forming a given concave/convexstructure on the surface of a medium to become an optical element. Sincethe physical cell is disposed so that its groove is directed forwardwhen each virtual cell of the three-dimensional virtual cell set 30shown in FIG. 5 is replaced with the physical cell as mentioned above, afinally formed optical element appears as a medium whose surface has aconcave/convex structure formed with many grooves. Therefore, thereplacement of the virtual cell with the physical cell is carried out asprocessing of providing data relative to a concave/convex pattern to adrawing device from a computer that stores information for each virtualcell (i.e., information that shows the specific amplitude and thespecific phase defined in each virtual cell) and then drawing theconcave/convex pattern onto the physical surface of the medium by thedrawing device. The processing of drawing a fine concave/convex patterncan be carried out by, for example, a patterning technique that uses anelectron beam drawing device. What is needed to mass-produce the sameoptical element is to form an original plate in which a desiredconcave/convex structure is formed by the drawing processing that usesan electron-beam drawing device, for example, and to transfer theconcave/convex structure onto many mediums by the stamping step thatuses the original plate.

The optical element according to the basic invention is basically formedwith a main body layer that is obtained by two-dimensionally arrangingthe physical cells shown in FIG. 8. However, a protective layer may beplaced on the surface of the main body layer if necessary. Thisprotective layer serves to cover the concave/convex surface formed inthe surface of the main body layer. The main body layer and theprotective layer are made of materials different from each other.

In a transmission type optical element in which incidence light given toeach physical cell passes through the main body layer and the protectivelayer and then turns into emission light, the main body layer and theprotective layer must be made of a transparent material and anothertransparent material, respectively, that are different in the refractiveindex. Here, let us consider a concrete relationship between the depthof the groove G and the phase when a transmission type optical element(i.e., transmission type physical cell) of a two-layer structure made ofsuch a main body layer and a protective layer is manufactured.

Now, let us consider a transmission type cell C(x, y) having a structureshown in the sectional view of the upside of FIG. 12. This is a cellhaving a two-layer structure made of a main body layer Ca in which agroove G whose depth is d(x, y) is formed and a protective layer Cbplaced on the upper surface thereof in such a way as to fill the grooveG. Herein, the refractive index of a material that forms the protectivelayer Cb (in other words, the refractive index of a material with whichthe concave part is filled or a material that constitutes the convexpart) is represented as n1, and the refractive index of a material thatforms the main body layer Ca is represented as n2. If the maximum depthdmax of the groove G (in other words, the maximum depth of the concavepart or the maximum height of the convex part) is set to bedmax=λ/|n1−n2|, a physical cell can be realized in which phasemodulation within the range of 0 through 2π can be applied to lightwhose wavelength is λ. For example, if the wavelength λ equals 400 nm(λ=400 nm) and the difference |n1−n2| in the refractive index equals 2,the maximum depth can be set to be dmax=200 nm (0.2 μm).

In this case, as shown in FIG. 12, the depth d(x, y) corresponding tothe specific phase θ(x, y) can be obtained by the following equations:If n1>n2,d(x, y)=λ·θ(x, y)/2(n1−n2)πand, if n1<n2,d(x, y)=dmax−λ·θ(x, y)/2(n2−n1)π

Accordingly, after the specific amplitude and specific phase of acertain virtual cell C(x, y) are obtained as A(x, y) and θ(x, y),respectively, the specific phase θ(x, y) is substituted for the aboveequation so as to calculate a corresponding depth d(x, y), and then aphysical cell that has a depth closest to the resulting depth d(x, y)and has a width closest to the dimension corresponding to the specificamplitude A(x, y) is selected from among the 28 kinds of physical cellsshown in FIG. 11, and the replacement of the virtual cell C(x, y) withthe selected physical cell is carried out. If the protective layer Cb isnot provided, the refractive index of air (almost 1) can be used as therefractive index n1 of the protective layer.

On the other hand, let us consider a reflection type cell C(x, y) havinga structure shown in the sectional view of the upside of FIG. 13. Thisis a cell having a two-layer structure made of a main body layer Cα inwhich a groove G whose depth is d(x, y) is formed and a protective layerCβ placed on the upper surface thereof in such a way as to fill thegroove G. In this cell, the boundary between the main body layer Cα andthe protective layer Cβ serves as a reflecting surface. The reflectanceon this reflecting surface is not necessarily to be 100%. The reflectingsurface may be a half-mirror having a reflectance of e.g. 50%. Thereflecting surface is also provided by inserting a half transparentlayer such as a transflector between the main body layer Cα and theprotective layer Cβ. Incidence light that has struck the protectivelayer Cβ from the upper side of the figure downward is reflected by thereflecting surface and is emitted upward in the figure. Herein, therefractive index of a material that forms the protective layer Cβ (inother words, the refractive index of a material with which the concavepart is filled or a material that constitutes the convex part) isrepresented as n. If the maximum depth dmax of the groove G (in otherwords, the maximum depth of the concave part or the maximum height ofthe convex part) is set to be dmax=λ/2n, a physical cell can be realizedin which phase modulation within the range of 0 through 2π can beapplied to light whose wavelength is λ. For example, if the wavelength λequals 400 nm (λ=400 nm) and the refractive index equals 2 (n=2), themaximum depth can be set to be dmax=100 nm (0.1 μm).

In this case, as shown in FIG. 13, the depth d(x, y) corresponding tothe specific phase θ(x, y) is obtained by the following equation:d(x, y)=λ·θ(x, y)/4nπ

If the protective layer Cβ is not provided, the refractive index of air(almost 1) can be used as the refractive index n of the protectivelayer. Accordingly, the maximum depth of the groove G can be set to bedmax=λ/2, and the depth d(x, y) corresponding to the specific phase θ(x,y) can be determined by the following equation:d(x, y)=λ·θ(x, y)/4π<<<§ 5. Modification in Consideration of Convenience of ReconstructiveEnvironment>>>

Let us now consider an environment in which reconstructing illuminationlight is projected onto the optical element manufactured according tothe method described above so as to reconstruct the object image 10recorded as a hologram. FIG. 14 is a side view showing the relationshipamong an optical element 40 (i.e., hologram-recording medium that usesphysical cells), reconstructing illumination light Lt or Lr, and aviewing point E that are used for the reconstruction. If the opticalelement 40 is a transmission type element that uses transmission typecells, the reconstructing illumination light Lt is projected to thesurface opposite to the viewing point E as shown in the figure, andlight that has passed through the optical element 40 is observed at theviewing point E. If the optical element 40 is a reflection type elementthat uses reflection type cells, the reconstructing illumination lightLr is projected to the surface on the same side as the viewing point Eas shown in the figure, and light that has been reflected from theoptical element 40 is observed at the viewing point E. In any case, whenthe optical element 40 is manufactured according to the above method,the most excellent reconstructed image can be obtained in the conditionthat the reconstructing illumination light Lt or Lr is given as a planewave of monochromatic light and projected in the normal direction to therecording surface (i.e., a two-dimensional array surface on whichphysical cells are arranged) of the optical element 40 as shown in FIG.14 (in other words, reconstructing illumination light is projected sothat the wave front becomes parallel with the recording surface of theoptical element 40), and the image is observed in the normal directionto the recording surface.

However, the actual reconstructive environment of the optical element 40where the object image 10 is recorded as a hologram does not necessarilylead to the ideal environment shown in FIG. 14. Especially, in the caseof the reflection type, since a head of an observing person is locatedat the position of the viewing point E, a shadow of the person, whichmakes the excellent reconstruction impossible, appears on the opticalelement 40 even if the reconstructing illumination light Lr is projectedfrom the direction shown in FIG. 14. Therefore, generally, the actualreconstructive environment has an aspect in which the reconstructingillumination light Lt or Lr is projected in the oblique direction withrespect to the recording surface of the optical element 40 so as toobserve the reconstructed image at the viewing point E located in thenormal direction as shown in FIG. 15, or, alternatively, an aspect inwhich the reconstructing illumination light Lt or Lr is projected in thenormal direction to the recording surface of the optical element 40 soas to observe the reconstructed image at the viewing point E located inthe oblique direction as shown in FIG. 16, or, alternatively, ant aspectin which both the projecting direction of the reconstructingillumination light Lt or Lr and the observing direction with respect tothe viewing point E are set as the oblique direction.

What is needed to manufacture the optical element 40 by which anexcellent reconstructed image can be obtained in the actualreconstructive environment is to carry out phase-correcting processingin which the specific phase defined for each virtual cell is corrected,in consideration of the direction of the illumination light projectedwhen reconstructed and the position of the viewing point whenreconstructed.

For example, let us consider a case in which, as shown in FIG. 17,reconstructing illumination light rays L1 through L4 are projected inthe oblique direction, and light rays LL1 through LL4 that haveundergone modulation of the amplitude and the phase as a result ofpassing through the optical element 40 (in other words, light rays LL1through LL4 have the reconstructed wave front of the object lightemitted from the object image 10) are observed at the viewing point Elocated in the normal direction. If the reconstructing illuminationlight rays L1 through L4 are each a monochrome plane wave whosewavelength is λ and if the reconstructing illumination light isprojected onto the optical element 40 in the oblique direction, anoptical path difference will have already arisen when the light reacheseach point P1 through P4 on the optical element 40, and incidence lightat each point P1 through P4 will have already generated a phasedifference. For example, the incidence light rays upon the positions ofpoints P2, P3, and P4 are longer in the optical path length by d2, d3,and d4, respectively, than the incidence light ray upon the position ofpoint P1. Therefore, the incidence light has already generated a phasedifference in proportion to the optical path difference. Therefore, ifthere is the supposition that “the optical element 40 is manufactured bywhich an excellent reconstructed image can be obtained in thereconstructive environment shown in FIG. 17”, the specific phase abouteach virtual cell can be calculated according to the above-mentionedmethod, and thereafter the processing of correcting each specific phasecan be carried out in accordance with the position of the cell. Forexample, there is no need to correct the cell located at the position ofpoint P1 of FIG. 17, and the cell located at the position of point P2undergoes the correction of the specific phase so as to cancel a phasedifference caused by the optical path difference d2. Accordingly, if theoptical element 40 is manufactured while carrying out the correction ofthe specific phase, an excellent reconstructed image can be given by thelight rays LL1 through LL4 emitted toward the viewing point E.

This corrective processing to the specific phase is likewise carried outin a case in which, as shown in FIG. 18, the reconstructing illuminationlight rays L1 through L4 are projected in the normal direction so as toobserve the light rays LL1 through LL4 that have undergone modulation ofthe amplitude and the phase as a result of passing through the opticalelement 40 (i.e., light that has reconstructed the wave front of theobject light from the object image 10) at the viewing point E located inthe oblique direction. That is, if the reconstructing illumination lightrays L1 through L4 are each a monochrome plane wave whose wavelength isλ and if the reconstructing illumination light rays are projected ontothe optical element 40 in the normal direction, no optical pathdifference occurs when the light ray reaches each point P1 through P4 onthe optical element 40, and the phases of the incidence light rays uponpoints P1 through P4 coincide with each other. However, a differencearises among the optical path lengths from points P1 through P4 to theviewing point E that the emission light emitted therefrom reaches, and aphase difference will arise when observed at the viewing point E. Forexample, the emission light rays from the positions of points P2, P3,and P4 are longer in the optical path length by d2, d3, and d4,respectively, than the emission light ray from the position of point P1.Therefore, the emission light has generated a phase difference inproportion to the optical path difference at the position of the viewingpoint E. Therefore, if there is the supposition that “the opticalelement 40 is manufactured by which an excellent reconstructed image canbe obtained in the reconstructive environment shown in FIG. 18”, thespecific phase about each virtual cell can be calculated according tothe above-mentioned method, and thereafter the processing of correctingeach specific phase can be carried out in accordance with the positionof the cell. For example, there is no need to correct the cell locatedat the position of point P1 of FIG. 18, and the cell located at theposition of point P2 undergoes the correction of the specific phase soas to cancel a phase difference caused by the optical path differenced2. Accordingly, if the optical element 40 is manufactured whilecarrying out the correction of the specific phase, an excellentreconstructed image can be provided by the light rays LL1 through LL4emitted toward the viewing point E.

The corrective processing to the specific phase for the transmissiontype optical element 40 was described above. The same principle of thecorrective processing applies to the reflection type optical element 40.

On the other hand, concerning the wavelength of the reconstructingillumination light, a case where monochromatic light whose wavelength isλ can be used as reconstructing illumination light is extremely rare inthe actual reconstructive environment, and therefore, normally, a casewhere the reconstruction is carried out under reconstructingillumination light close to white can be regarded as general. If thereconstruction is carried out by use of reconstructing illuminationlight that includes a plurality of wavelength components, differentphase modulation is performed for light having each individualwavelength, and therefore an excellent reconstructed image cannot beobtained. Concretely, a reconstructed image is formed as if images withvarious colors are superimposed on each other with slight incongruity.

Therefore, in order to obtain a fairly excellent reconstructed imageeven in the reconstructive environment that uses white reconstructingillumination light, a method, such as that shown in FIG. 19, should beapplied when a complex amplitude distribution of object light iscalculated. Like the system shown in FIG. 5, a system shown in FIG. 19is used to define the object image 10 and the three-dimensional virtualcell set 30 on a computer and calculate for obtaining a distribution ofthe totaled complex amplitude of each object light emitted from theobject image 10 on the three-dimensional virtual cell set 30. Herein,the three-dimensional virtual cell set 30 is constructed by arrangingvirtual cells horizontally and vertically, and is a cell set thatconsists of the virtual cells arranged on the two-dimensional matrix.Representative points are defined in the virtual cells, respectively.

When the technique described herein is employed, the totaled complexamplitude at the position of each representative point is calculated bythe following method. First, a plurality of M point-light-source rowseach of which extends horizontally and which are mutually arrangedvertically are defined on the object image 10. In the example of thefigure, M=3, and three point light source rows m1, m2, and m3 aredefined. Each point light source row includes a plurality of point lightsources arranged horizontally. For example, a point light source row m1includes j point light sources O(m1,1), O(m1,2), . . . , O(m1,j). On theother hand, on the side of the three-dimensional virtual cell set 30, Mgroups in total are defined by defining groups of virtual cells thatbelong to a plurality of rows contiguous vertically as one group in thetwo-dimensional matrix. In the example of the figure, three groups intotal are defined as M=3. That is, a first group g1 consists of virtualcells that belong to first through third rows, a second group g2consists of virtual cells that belong to fourth through sixth rows, anda third group g3 consists of virtual cells that belong to sevenththrough ninth rows.

The M point light source rows are thus defined on the side of the objectimage 10, and the M groups are defined on the side of thethree-dimensional virtual cell set 30. Thereafter, the M point lightsource rows and the M groups are caused to correspond to each other inaccordance with the arrangement order concerning the vertical direction.That is, in the example of the figure, the uppermost point light sourcerow m1 is caused to correspond to the uppermost group g1, the middlepoint light source row m2 is caused to correspond to the middle groupg2, and the lowermost point light source row m3 is caused to correspondto the lowermost group g3. Thereafter, on the supposition that theobject light emitted from a point light source in the m-th point lightsource row (m=1 to M) reaches only the virtual cell that belongs to them-th group, the totaled complex amplitude at the position of eachrepresentative point is calculated. For example, the object lightemitted from the point light sources O(m1,1), O(m1,2), . . . , O(m1,j)that belong to the point light source row m1 in FIG. 19 is regarded asreaching only the virtual cells that belongs to the group g1 (virtualcells arranged in the first to third rows), and as not reaching thevirtual cells that belongs to the groups g2 and g3, and the totaledcomplex amplitude is calculated. In other words, the calculation of thetotaled complex amplitude at the position of the representative point ofthe virtual cell that belongs to the group g1 is carried out inconsideration of only the object light emitted from the point lightsources O(m1,1), O(m1,2), . . . , O(m1,j) that belong to the point lightsource row m1, not in consideration of the object light emitted from thepoint light sources that belong to the point light source rows m2 andm3.

Actually, the object image 10 cannot be recorded as an original hologramif it is recorded under these conditions. After all, the basic principleof the hologram resides in that all information for the object image 10is recorded onto any places of the recording surface, and thereby astereoscopic image can be reconstructed. If the object image 10 isrecorded under the conditions mentioned above, only information of apart of the point-light-source row m1 (i.e., part of the upper portionof the object image 10) is recorded in the area of the group g1. As aresult, a stereoscopic reconstructed image as an original hologramcannot be obtained. Concretely, stereoscopic vision relative to thehorizontal direction can be given, but stereoscopic vision relative tothe vertical direction becomes insufficient. However, if the objectimage 10 is recorded under these conditions, a more excellentreconstructed image (i.e., an even clearer reconstructed image includingthe fact that the stereoscopic vision relative to the vertical directionis insufficient) can be obtained in the reconstructive environment thatuses white reconstructing illumination light. The reason is that, whenreconstructed, an effect to control the wavelength distribution of thereconstructing light concerning with the vertical direction can beobtained by recording the object image 10 in such a way as to divide itinto parts concerning with the vertical direction.

<<<§ 6. Points of Improvement of an Optical Element of the PresentInvention>>>

Though specific examples of the arrangement of the optical element usingthree-dimensional cells, disclosed as a basic invention in theabove-mentioned U.S. Pat. No. 6,618,190, have been described above, withthis optical element, since noise components become mixed in duringreconstruction, clear reconstruction results cannot be obtainednecessarily. This is because a part of the incident light that isprovided as illumination light in the reconstruction process or a partof the reflected light of this incident light is observed as 0th-orderdiffraction light. The cause as to why this 0th-order diffraction lightis observed shall now be described.

With a transmission type three-dimensional cell C(x, y) shown in FIG. 9,amplitude information is recorded as width G1 of a groove G(x, y) andphase information is recorded as depth G2 of groove G(x, y) because, asdescribed above, when a light L1, which has been made incident on aninternal surface S1 of groove G(x, y), is observed as transmitted light,the intensity of this transmitted light depends on the area (that is,width G1 of groove G(x, y)) of surface S1 and the phase of thistransmitted light depends on the optical path length of passage throughthe medium of refractive index n2 (that is, depth G2 of groove G(x, y)).Meanwhile, a light L2, which is made incident on an external surface S2of groove G(x, y), is not subject to modulation by groove G(x, y).Emitted light L2 thus does not contain any phase components ofsignificance, and even if such emitted light L2 is observed at a viewingpoint position in a reconstruction process, it is observed only as aso-called background noise component and is not recognized as effectivelight for reconstruction of an image of any significance.

The same applies to a reflection type three-dimensional cell C(x, y)shown in FIG. 10. When a light L1, which has been made incident on aninternal surface S1 of groove G(x, y), is observed as reflected light,the intensity of this reflected light depends on the area (that is,width G1 of groove G(x, y)) of surface S1 and the phase of thisreflected light depends on the optical path length of passage throughthe medium of refractive index n1 (that is, depth G2 of groove G(x, y)).Reflected light L1, which is observed at a viewing point position, thuscontains amplitude information, which is recorded as width G1, and phaseinformation, which is recorded as depth G2. Meanwhile, a light L2, whichis made incident on an external surface S2 of groove G(x, y), is notsubject to modulation by groove G(x, y). Reflected light L2 thus doesnot contain any phase components of significance, and even if suchreflected light L2 is observed at a viewing point position in areconstruction process, it is observed only as a so-called backgroundnoise component and is not recognized as effective light forreconstruction of an image of any significance.

Emitted light L2 in the example shown in FIG. 9 and reflected light L2in the example shown in FIG. 10 are thus components corresponding tobeing 0th-order diffraction light. Whereas light L1, which is modulatedby groove G(x, y), is light that is observed as a signal component,light L2 (0th-order diffraction light), which is not modulated by grooveG(x, y), is light that is observed as a noise component. Since thisnoise component light does not contain information of any significance,it is recognized simply as background noise by an observer, and ispreferably eliminated in order to obtain a clear image with a low amountof noise components. An object of the present invention is to restrainthe generation of light L2 (0th-order diffraction light), which isobserved as a noise component, as much as possible. Specific methods forthis purpose shall now be described by way of several embodiments.

(1) First Groove Type Embodiment

FIG. 21 is a perspective view of an example of the structure of aphysical cell C1(x, y) of a first groove type embodiment of the presentinvention, and FIG. 22 is a sectional view of this physical cell(hatching of the main body portion of the cell is omitted). Though thisphysical cell C1(x, y) has substantially the same structure as physicalcell C(x, y), shown in FIG. 8, it differs in having light blockinglayers F1 and F2 formed at portions besides a groove G(x, y) on theupper surface. In the present example, light blocking layers F1 and F2 are films formed of chromium and thickness C4 of each is approximately0.2 μm. Needless to say, the material and thickness of light blockinglayers F1 and F2 are not restricted in particular as long as theselayers provide an adequate light blocking function.

The function of light blocking layers F1 and F2 is made clear in thesectional view of FIG. 22. Like physical cell C(x, y), shown in FIG. 9,the present physical cell C1(x, y) is a transmission type cell, andlight L1 that is transmitted through the interior of groove G(x, y) isobserved as modulated light. However, light L2, which is illuminatedoutside groove G(x, y), is blocked by light blocking layer F1 or F2 andprevented from propagating into the interior of the cell. Lightreflecting films or light absorbing films may be used as light blockinglayers F1 and F2. In the former case, light L2, which is illuminatedfrom above onto light blocking layer F1 or F2, is reflected upward, andin the latter case, the light is absorbed. In either case, light L2 willnot proceed inside the cell. Needless to say, light blocking layers F1and F2 may be formed of films having both the properties of a lightreflecting film and the properties of a light absorbing film. Forpractical use, light blocking layers F1 and F2 may be formed, forexample, of a chromium film.

The same applies in the opposite case where light is illuminated fromthe lower side of the figure and is observed at the upper side. Thoughlight that is transmitted through the interior of groove G(x, y) isobserved at the upper side, light outside groove G(x, y) is blocked bylight blocking layer F1 or F2.

Physical cell C1(x, y), shown in FIG. 21 and FIG. 22, is thus formed ofa light transmitting material, has a specific amplitude and a specificphase defined therein, and has a first region (internal region of thegroove through which light L1 is transmitted), which is a portion havingan area that is in accordance with the specific-amplitude defined in thecell, and a second region (region lying outside the groove and ontowhich light L2 is illuminated), which comprises the portions except thefirst region, defined on the upper surface of the cell, with the firstregion being formed by the bottom surface of groove G(x, y), having adepth that is in accordance with the specific phase defined in the cell,and light blocking layers F1 and F2 being formed on the second region.The cell itself thus has specific optical characteristics such that whena predetermined incident light is provided to the upper surface or thelower surface of the cell, transmission emitted light, with which theamplitude and phase of the incident light have been changed inaccordance with the specific amplitude and specific phase defined in thecell, is obtained from the lower surface or the upper surface of thecell.

By thus providing light blocking layers F1 and F2, light L2 (0th-orderdiffraction light), which is observed as a noise component, can beblocked and just light L1, which is observed as a signal component, canbe guided selectively to the observation point. A clear reconstructedimage with a low amount of noise components can thus be obtained.

By arranging light blocking layers F1 and F2 as light absorbing layersand arranging the bottom surface of groove G(x, y) to form a reflectingsurface, physical cell C1(x, y), shown in FIG. 21 and FIG. 22, can beused as a reflection type cell that is based on the principlesillustrated in FIG. 10 (a cell of the type with which illuminationreconstruction light is illuminated from the upper side and observationis performed from the upper side). That is, whereas light L1, which isreflected by the bottom surface of groove G(x, y), is observed as asignal component light, light L2, which is illuminated outside grooveG(x, y), is absorbed by light absorbing layers F1 and F2 and observationof light L2, which is a noise component, can thus be restrained.

(2) Second Groove-Type Embodiment

FIG. 23 is a perspective view of an example of the structure of aphysical cell C2(x, y) of a second groove type embodiment of the presentinvention, and FIG. 24 is a sectional view of this physical cell(hatching of the main body portion of the cell is omitted). Though thisphysical cell C2(x, y) has substantially the same structure as physicalcell C(x, y), shown in FIG. 8, it differs in having light absorbinglayers F3 and F4 formed at portions of the upper surface besides grooveG(x, y) and having a light reflecting layer F5 formed on the lowersurface. In the present example, light absorbing layers F3 and F4 arefilms formed of chromium and thickness C4 of each is approximately 0.2μm. Light reflecting layer F5 is a film formed of aluminum and thicknessC5 thereof is approximately 0.2 μm. Needless to say, the materials andthicknesses of light absorbing layers F3 and F4 and light reflectinglayer F5 are not restricted in particular as long as these layersprovide adequate light absorbing and reflecting functions.

The functions of light absorbing layers F3 and F4 and light reflectinglayer F5 are made clear in the sectional view of FIG. 24. The presentphysical cell C2(x, y) is a reflection type cell, and light L1, which istransmitted through the interior of groove G(x, y), propagates insidethe cell, is directed upward by being reflected by light reflectinglayer F5, and is observed as modulated light. However, light L2, whichis illuminated outside groove G(x, y), is absorbed by light absorbinglayers F3 and F4.

Physical cell C2(x, y), shown in FIG. 23 and FIG. 24, is thus formed ofa light transmitting material, has a specific amplitude and a specificphase defined therein, and has a first region (internal region of thegroove through which light L1 is transmitted), which is a portion havingan area that is in accordance with the specific amplitude defined in thecell, and a second region (region lying outside the groove and ontowhich light L2 is illuminated), which comprises the portions except thefirst region, defined on the upper surface of the cell, with the firstregion being formed by the bottom surface of groove G(x, y), having adepth that is in accordance with the specific phase defined in the cell,light absorbing layers F3 and F4 being formed on the second region, andthe light reflecting layer being formed on the lower surface of thecell. The cell itself thus has specific optical characteristics suchthat when a predetermined incident light is provided from the uppersurface of the cell, reflection emitted light, with which the amplitudeand phase of the incident light have been changed in accordance with thespecific amplitude and specific phase defined in the cell, is obtainedfrom the upper surface of the cell.

By thus providing light absorbing layers F3 and F4, light L2 (0th-orderdiffraction light), which is observed as a noise component, can beblocked and just light L1, which is observed as a signal component, canbe guided selectively to the observation point. A clear reconstructedimage with a low amount of noise components can thus be obtained.

(3) Third Groove Type Embodiment

FIG. 25 is a perspective view of an example of the structure of aphysical cell C3(x, y) of a third groove type embodiment of the presentinvention and FIG. 26 is a sectional view of this physical cell(hatching of the main body portion of the cell is omitted). As withphysical cell C2(x, y), shown in FIG. 23 and FIG. 24, the presentphysical cell C3(x, y) has light absorbing layers F3 and F4 formed atportions of the upper surface besides groove G(x, y). However, whereasphysical cell C2(x, y) has light reflecting layer F5 formed on the lowersurface of the cell, physical cell C3(x, y) differs in having a lightreflecting layer F6 formed on the bottom surface of groove G(x, y).Light absorbing layers F3 and F4 are films formed of chromium in thepresent example as well and thickness C4 of each layer is approximately0.2 μm. Light reflecting layer F6 is a film formed of aluminum andthickness thereof is approximately 0.2 μm. Needless to say, thematerials and thicknesses of light absorbing layers F3 and F4 and lightreflecting layer F6 are not restricted in particular as long as theselayers provide adequate light absorbing and reflecting functions.

The functions of light absorbing layers F3 and F4 and light reflectinglayer F6 are made clear in the sectional view of FIG. 26. The presentphysical cell C3(x, y) is a reflection type cell, and light L1, which isilluminated from the lower side, propagates inside the cell, is directeddownward by being reflected by light reflecting layer F6 at the bottompart of groove G(x, y), and is observed as modulated light at anobservation point at the lower side. However, light L2, which isilluminated outside groove G(x, y), propagates inside the cell andbecomes absorbed by light absorbing layers F3 and F4.

Physical cell C3(x, y), shown in FIG. 25 and FIG. 26, is thus formed ofa light transmitting material, has a specific amplitude and a specificphase defined therein, and has a first region (internal region of thegroove that is reached by light L1), which is a portion having an areathat is in accordance with the specific amplitude defined in the cell,and a second region (region lying outside the groove and being reachedby light L2), which comprises the portions except the first region,defined on the upper surface of the cell, with the first region beingformed by the bottom surface of groove G(x, y), having a depth that isin accordance with the specific phase defined in the cell, lightabsorbing layers F3 and F4 being formed on the second region, and lightreflecting layer F6 being formed on the first region. The cell itselfthus has specific optical characteristics such that when a predeterminedincident light is provided from the lower surface of the cell,reflection emitted light, with which the amplitude and phase of theincident light have been changed in accordance with the specificamplitude and specific phase defined in the cell, is obtained from thelower surface of the cell.

By thus providing light absorbing layers F3 and F4, light L2 (0th-orderdiffraction light), which is observed as a noise component, can beblocked and just light L1, which is observed as a signal component, canbe guided selectively to the observation point. A clear reconstructedimage with a low amount of noise components can thus be obtained.

Though with the example shown in FIG. 25 and FIG. 26, light reflectinglayer F6 is formed just near the bottom part of groove G(x, y), thereare no restrictions in regard to the thickness of light reflecting layerF6. For example, with a physical cell C4(x, y), shown in FIG. 27, alight reflecting layer F7, with a thickness suited for filling theentirety of the interior of groove G(x, y), is formed. Also, a physicalcell C5(x, y), shown in FIG. 28, is an example wherein an even thickerlight reflecting layer F8 is formed. This light reflecting layer F8 hasa structure that covers the upper surfaces of light absorbing layers F3and F4 by a thickness C6.

(4) Fourth Groove Type Embodiment

FIG. 29 is a perspective view of an example of the structure of aphysical cell CC(x, y) of a fourth groove type embodiment of the presentinvention and FIG. 30 is a sectional view of this physical cell. As withphysical cell C1(x, y), shown in FIG. 21 and FIG. 22, the presentphysical cell CC(x, y) is a transmission type cell and has a lightabsorbing layer F9 formed at portions of the upper surface besides agroove GG(x, y). However, whereas groove G(x, y) of each of the previousembodiments is formed to pass through from the front to the rear of themain cell body, the present groove GG(x, y) has a structure that isformed by hollowing a central portion of the main cell body and grooveGG(x, y) is surrounded by the main cell body at four sides. In the caseof the illustrated example, groove GG(x, y) has a square opening witheach side being of dimension G1.

Physical cell CC(x, y), shown in FIG. 29, though differing somewhat inshape from physical cell C1(x, y), shown in FIG. 21, is exactly the samein essential function as physical cell C1(x, y). That is, a first region(the bottom surface of groove GG(x, y) having a square opening with eachside being of dimension G1), which is a portion having an area that isin accordance with the specific amplitude defined in the cell, and asecond region, which comprises the portion (square-frame-like portionsurrounding the opening) besides the first region, are defined on theupper surface of the cell, and light blocking layer F9 is formed on thesecond region. Each individual cell thus has specific opticalcharacteristics such that when a predetermined incident light isprovided to the upper surface or the lower surface of the cell,transmission emitted light, with which the amplitude and phase of theincident light have been changed in accordance with the specificamplitude and specific phase defined in the cell, is obtained from thelower surface or the upper surface of the cell. That is, whereas lightthat is transmitted through the interior of groove GG(x, y) reaches anobservation point as transmission emitted light upon being modulated inaccordance with the specific amplitude and specific phase, light that isilluminated outside groove GG(x, y) is blocked by light blocking layerF9 and is restrained from being observed as a noise component.

Though just a transmission type physical cell was described here, areflection type physical cell having a groove GG(x, y) such as shown inFIG. 29 can also be realized.

(5) Convex Type Embodiments

Though examples, wherein a physical cell is arranged by forming a groovein a main cell body part, were described above, in carrying out thepresent invention, a convex part may be provided in place of a groove.FIG. 31 is a perspective view of an example of the structure of aphysical cell C6(x, y) of a first convex type embodiment of the presentinvention, and FIG. 32 is a sectional view of this physical cell(hatching of the main body portion of the cell is omitted). Physicalcell C6(x, y) shown here has substantially the same structure asphysical cell C1(x, y) shown in FIG. 21 but differs in having a convexpart B(x, y) formed in place of groove G(x, y). As illustrated, convexpart B(x, y) is a rectangular parallelepiped structure with a width B1,a height B2, and a length B3. Here, area B1×B3 is set to a value that isin accordance with a specific amplitude defined in the cell and heightB2 is set to a value that is in accordance with a specific phase definedin the cell. As with physical cell C1(x, y), shown in FIG. 21, lightblocking layers F1 and F2 are formed at portions of the cell's uppersurface besides convex part B(x, y). As shown in FIG. 32, whereas lightL1, which has been transmitted through the interior of convex part B(x,y) becomes observed as a signal component, light L2, which isilluminated outside convex part B(x, y) is blocked by light blockinglayers F1 and F2 and will not be observed as a noise component.

Physical cell C6(x, y), shown in FIG. 31 and FIG. 32, can also be usedas a reflection type cell based on the principles shown in FIG. 10 (atype of cell with which illumination reconstruction light is illuminatedfrom the upper side and observation is made from the upper side). Thatis, by arranging light blocking layers F1 and F2 as light absorbinglayers and arranging the upper surface of convex part B(x, y) to be areflecting surface, whereas light L1, which is reflected by the uppersurface of convex part B(x, y) can be observed as a signal componentlight, light L2 that is illuminated outside convex part B(x, y) isabsorbed by light blocking layers F1 and F2 and observation of light L2as a noise component can thus be restrained.

FIG. 33 is a sectional view of an example of the structure of a physicalcell C7(x, y) of a second convex type embodiment of the presentinvention. Physical cell C7(x, y) shown here has substantially the samestructure as physical cell C2(x, y) shown in FIG. 24 but differs inhaving convex part B(x, y) formed in place of groove G(x, y). Also, FIG.34 is a sectional view of an example of the structure of a physical cellC8(x, y) of a third convex type embodiment of the present invention.Physical cell C8(x, y) shown here has substantially the same structureas physical cell C3(x, y) shown in FIG. 26 but differs in having convexpart B(x, y) formed in place of groove G(x, y). In all cases, thedifference is just due to having groove G(x, y) or having convex partB(x, y) and the basic functions are the same.

Also, though unillustrated here, a convex type embodiment provided witha convex part in place of groove GG(x, y) can be realized in regard tophysical cell CC(x, y), shown in FIG. 29.

<<<§ 7. Method for Manufacturing an Optical Element of the PresentInvention>>>

Lastly, an example of a method for manufacturing the optical element ofthe present invention shall be described. As was described in § 6, theoptical element of the present invention is arranged by aligning aplurality of three-dimensional cells. Each cell has a specific amplitudeand a specific phase defined therein, has a groove part or a convex partformed in accordance with the specific amplitude and the specific phase,and requires that a light blocking layer, light absorbing layer, lightreflecting layer, etc., be formed at portions of the upper surfaceexcept the groove part or the convex part.

A semiconductor manufacturing art is preferably employed to mass-producean optical element with such characteristics in an industrial scale.Semiconductor manufacturing arts are suited for fine processing and arealso suited for industrial mass production. An example of a method formanufacturing the optical element of the present invention shall now bedescribed for a model illustrated by the sectional view of FIG. 35. Themodel shown in FIG. 35 is that of a simple optical element, wherein fourkinds of three-dimensional cells are aligned one-dimensionally. Thoughobviously such a simple optical element cannot provide the function of aproper optical element, an example of a manufacturing process shall bedescribed here based on such a simple model here for the sake ofconvenience of description.

In the optical element shown in FIG. 35, four cells of the same type astransmission type physical cell C1(x, y), shown in FIG. 21, are aligned,and in each of the four cells CL1 to CL4, a specific amplitude and aspecific phase are defined. That is, each specific amplitude correspondsto the area of the opening of a groove and each specific phasecorresponds to the depth of a groove. Also, light blocking layers F1 andF2 are formed at the surroundings of the grooves. Cell CL1 has formedtherein a groove with a width a1 and a depth 0 (that is, a groove ispractically not formed), cell CL2 has formed therein a groove with awidth a2 and a depth d, cell CL3 has formed therein a groove with awidth, a3 and a depth 2 d, and cell CL4 has formed therein a groove witha width a4 and a depth 3 d. Here, it shall be deemed that the main bodypart of each cell is formed of a quartz glass substrate and lightblocking layers F1 and F2 are formed of a chromium layer.

An example of a process of manufacturing such an optical element shallnow be described based on the sectional views of FIG. 36 and FIG. 37.First, as shown in FIG. 36A, a quartz glass substrate 100, which is tobecome the main cell body part, is prepared and a chromium layer 200 isformed over the entire upper surface. Sputtering, vapor deposition, orother general method may be used to form chromium layer 200. A resistlayer 300 is then formed on the upper surface of chromium layer 200, andusing a predetermined exposure mask, just the groove-forming regions ofcells CL3 and CL4, at which grooves of depths 2 d and 3 d are requiredto be formed, are exposed. This resist layer 300 is developed and afterremoving the exposed parts, the remaining resist layer 300 is used as amask and etching of chromium layer 200 is performed. FIG. 36A shows thestate upon completion of such etching. Openings H3 and H4 are thusformed in resist layer 300 and chromium layer 200. Here, opening H3 isformed at the position of the groove that is to be formed in cell CL3,and opening H4 is formed at the position of the groove that is to beformed in cell CL4. A general method, such as dry etching using achlorine-based gas or wet etching using perchloric acid and cerium (IV)diammonium nitrate, may be used to etch chromium layer 200.

Etching of quartz glass substrate 100 is then performed in the stateshown in FIG. 36A to form grooves of depth 2 d at the portions ofopenings H3 and H4. FIG. 36B shows the state upon completion of suchetching. A groove of depth 2 d is formed at both the portion of openingH3 and the portion of opening H4. Such etching can be carried out by adry etching process using CF₄ or other fluorine-based gas. When thegrooves are thus formed, resist layer 300 is peeled off once at thispoint. FIG. 36C shows the state after the peeling off of resist layer300.

A resist layer 400 is then formed on the entire upper surface of thesubstrate again. FIG. 37A shows the state immediately after the formingof resist layer 400. As illustrated, resist layer 400 fills even theinteriors of the grooves that have been formed in the previous steps.Then using a predetermined exposure mask on this resist layer 400, justthe groove-forming regions of cells CL2 and CL4 are exposed. When thisresist layer 400 is exposed and the exposed parts are removed, the stateshown in FIG. 37B is reached in which openings H2 and H4 are formed.Here, opening H2 is formed at the position of the groove that is to beformed in cell CL2 and opening H4 is formed at the position of thegroove that is to be formed in cell CL4. By then performing etching onchromium layer 200 again, the chromium layer 200 inside opening H2 canbe removed. Etching of quartz glass substrate 100 is thus performedagain on the internal regions of openings H2 and H4 to hollow theportions of openings H2 and H4 by just a depth d. FIG. 37C shows thestate upon completion of such etching. A groove of depth d is formed atthe portion of opening H2, and at the portion of opening H4, a groove ofdepth 3 d is formed by the groove of depth 2 d, which existedoriginally, being hollowed further by just depth d.

Lastly, the portion of resist layer 400 at the position of the groove tobe formed in cell CL1 is exposed and removed to form an opening H1 andthe chromium layer 200, corresponding to this opening H1, is removed byetching. In the final stage, by peeling off the entire remaining resistlayer 400, the structure shown in FIG. 37D can be obtained. Thisstructure is none other than the optical element shown in FIG. 35.

With the above-described manufacturing process, chromium layer 200 canbe used as the mask in the step of etching quartz glass substrate 100,and moreover, chromium layer 200 that remains at the final stage can beused as the light blocking layer that is formed on the upper surface ofthe cells. The process of exposing the resist layer will be a process ofexposing a considerably fine pattern. Thus for practical purposes, anelectron beam drawing device is preferably used. Also, though a processof forming cells with four different depths (0, d, 2 d, and 3 d) wasdescribed with the above example, in the case where cells of a largernumber of types of depths are to be formed, the process of etchingquartz glass substrate 100 is repeated further.

With the optical element of the present invention, since each individualthree-dimensional cell has a function of recording both an amplitude anda phase, both the amplitude and phase that are recorded in eachindividual cell can be reproduced in the reconstruction process. Theoptical element of the present invention can thus be used not only as ahologram for reconstructing a three-dimensional image but can also beused as an optical element in various applications. For example, thisoptical element can be used in such applications as a beam shaper, anoptical branching element, an optical element for an exposure device, aprocessing mask, a directional diffuser plate, a directional reflectionplate, an image projecting element, and an image synthesizing element(glasses, fan, camera filter, etc.) as well.

1. An optical element comprising a set of a plurality ofthree-dimensional cells: wherein an individual cell has a specificamplitude and a specific phase defined therein; a first region,comprising a portion with an area that is in accordance with thespecific amplitude defined in the individual cell, and a second region,comprising a portion except the first region, are defined on an uppersurface of the individual cell, the first region on the upper surface ofthe individual cell being formed by a convex part, having a height thatis in accordance with the specific phase defined in the individual cell,a top surface of the convex part being a reflecting surface and a lightabsorbing layer being formed on the second region on the upper surfaceof the individual cell; and the individual cell has a specific opticalcharacteristic such that when predetermined incident light is providedfrom the upper surface of the cell, reflection emitted light, with whichamplitude and phase of the incident light have been changed inaccordance with the specific amplitude and the specific phase defined inthe cell, is obtained from the upper surface of the cell.
 2. The opticalelement according to claim 1, wherein: an individual cell is arranged byforming, on a base having a first rectangular parallelepiped shape, aconvex part with a second rectangular parallelepiped shape that issmaller than the first rectangular parallelepiped shape.
 3. The opticalelement according to claim 2, wherein: individual cells are aligned in aform of a two-dimensional matrix with respective upper surfaces beingdirected upward.
 4. The optical element according to claim 1, wherein: acomplex amplitude distribution of object light from an object image isrecorded so that the object image is reconstructed upon observation froma predetermined viewing point position thus to use said optical elementas a hologram.
 5. An optical element comprising a set of a plurality ofthree-dimensional cells: wherein an individual cell is made of a lighttransmitting material and has a specific amplitude and a specific phasedefined therein; a first region, comprising a portion with an area thatis in accordance with the specific amplitude defined in the individualcell, and a second region, comprising a portion except the first region,are defined on an upper surface of the individual cell, the first regionon the upper surface of the individual cell being formed by a convexpart, having a height that is in accordance with the specific phasedefined in the individual cell, a light absorbing layer being formed onthe second region on the upper surface of the individual cell, and alight reflecting layer being formed on the first region on the uppersurface of the individual cell; and the individual cell has a specificoptical characteristic such that when predetermined incident light isprovided from a lower surface of the cell, reflection emitted light,with which amplitude and phase of the incident light have been changedin accordance with the specific amplitude and the specific phase definedin the cell, is obtained from the lower surface of the cell.
 6. Theoptical element according to claim 5, wherein: an individual cell isarranged by forming, on a base having a first rectangular parallelepipedshape, a convex part with a second rectangular parallelepiped shape thatis smaller than the first rectangular parallelepiped shape.
 7. Theoptical element according to claim 6, wherein: individual cells arealigned in a form of a two-dimensional matrix with respective uppersurfaces being directed upward.
 8. The optical element according toclaim 6, wherein: a complex amplitude distribution of object light froman object image is recorded so that the object image is reconstructedupon observation from a predetermined viewing point position thus to usesaid optical element as a hologram.